Solving Infinite Cylinder Homework w/ Electric Field Inside Void

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The discussion revolves around solving a physics homework problem involving an infinitely large charged dielectric cylinder with a cylindrical void. The key point is that the electric field inside the void can be determined by superimposing the electric fields from two cylinders with opposite charge densities. Although one participant expresses doubt about using Gauss's law, it is clarified that it can indeed be applied to calculate the field at any point within the uniformly charged cylinder. The resulting electric field inside the void is homogeneous, meaning it has the same magnitude and direction throughout. The solution emphasizes the importance of understanding the principles of superposition and Gauss's law in electrostatics.
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Homework Statement


In an infinitely large evenly charged dielectric cylinder(charge density is \rho ) there is an infinitely large cylindrical void. Prove that the electric field inside the void is homogenous and find its value. (picture)
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Homework Equations


The Attempt at a Solution


I don't think i can use Gauss law here. Any ideas ?
 
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You can calculate the field at any point (radius) in a uniformly charged cylinder using Gauss's law. Now add 2 cylinders, one big and one small, of opposite charge densities to create the hole. The field within is the sum of the fields within each cylinder.
 

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